C341518

Dr.M.T Bhoite, Swapnil Gavhane, Mitali Gore, Sukanya Kanjvane / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp. 15-18
15 | P a g e
Numerical and Experimental Investigations On Various Fin
Configurations subjected to Isoflux Heating under the Influence
of Convective Cooling
Dr.M.T Bhoite1
, Swapnil Gavhane, Mitali Gore, Sukanya Kanjvane
(Department of Mechanical Engineering, MIT Academy of Engineering,Alandi, Pune, Maharashta, Pune-
412105)
ABSTRACT
Present paper aims at numerical and
experimental assessment of thermal performance
of various fin arrays. The numerical results are
obtained by FLUENT code which uses standard
discretization practices of spatial, temporal and
convective derivatives in mass, momentum and
energy transport equations. Results are reported
in terms of the variation of heat transfer
coefficient and Nusselt number with the respect to
Reynolds number.
Keywords - Effectiveness, Fins, Nusselt number,
Reynolds number,
I. INTRODUCTION
Pinfins are extended surfaces used to
enhance heat transfer by availing additional area for
heat transport and introducing flow patterns
contributing to enhancement of heat transport.
Ellison [1] and Kraus and Bar-Cohen [2] have
presented the fundamentals of heat transfer and
hydrodynamics characteristics of heat sinks
including the fin efficiency, forced convective
correlations, applications in heat sinks, etc.
Electronic cooling is one of the major application of
pinfins. Researchers like Iyengar and Bar-Cohen [3]
determined the least-energy optimization of plate fin
heat sinks in the status of forced convection.
Investigations are also carried out regarding shape
optimization of array of pin-fins as done by Park et
al. [4]
Fin efficiency and convection effectiveness
can be examined to minimize any significant
conduction resistance though the fins and improve
the overall performance of the heat sink. There
exists significant work carried out in the thermal
analysis of heat sink design. An analytical approach
was taken by Keyes [5] who developed formulas for
the fin and channel dimensions that provide
optimum cooling under various forced convection
cooling conditions.
In the present study, the objective is to
numerically investigate the performance of fin
arrays consisting of circular, square shaped fins. The
array of fin is having inline configuration without
any staggering. The analysis is carried out using
numerical simulations and experimentations.
II. MATHEMATICAL FORMULATION
A base plate of 88 X 88 X 8 mm is
subjected to isoflux heating and the fins are attached
on the top surface in in-line manner. Fins used are of
two types viz. circular and square shaped having 35
mm height. The set of 25 fins in order pattern 5 X 5
are used to enhance the heat transfer. The assembly
of plates and fins is enclosed in a rectangular duct
sixe of 400 X 88 X 180 mm. It can be observed that
dimensions of the duct are maintained sufficiently
large such that flow is undisturbed by end effects.
In order to make a comparison , some parameters
are fixed for all geometries. These are: (i) Same
pitch pitch (Px=Py) (ii) the area for air flow passage
per base area. The commonly used in-line circular
array of fins with 8 mm pin diameter (w) and a 16
mm pitch has been selected to be the base case for
comparison.
To analyze the flow and temperature
distributions in geometry, set of partial differential
equations namely, solve momentum (Navier-Stoke’s
equations), continuity,energy transport equation are
to be solved using numerical algorithms subjected to
appropriate boundary conditions alongwith turbulent
kinetic energy and turbulent dissipation rate
equations.
Continuity Equation:
∂u/∂x + ∂v/∂y + ∂w/∂z = 0 (1)
X-direction momentum equation:
ρDu/Dt = - ∂p/∂x + ∂/∂x ( µ + µt ( 2∂u/∂x)) +
∂/∂y(µ + µt (∂ u/∂y + ∂ v/∂x ) + ∂/∂z(µ + µt (∂
u/∂z + ∂ w/∂x ) + ρgx (2)
Y-direction momentum equation:
ρDv/Dt = - ∂p/∂y + ∂/∂x ( µ + µt (∂u/∂y + ∂v/∂x) )
+ ∂/∂y(µ + µt (2∂v/∂y ) + ∂/∂z(µ + µt (∂ v/∂z + ∂
w/∂y ) + ρgy (3)
Z-direction momentum equation:
ρDw/Dt = - ∂p/∂y + ∂/∂x ( µ + µt (∂u/∂z + ∂w/∂x) )
+ ∂/∂y(µ + µt ( ∂v/∂z + ∂w/∂y ) + ∂/∂z(µ + µt (2∂
w/∂z ) + ρgz (4)
Energy equation (As applied to solid and fluid):
ρCp DT/Dt = ∂/∂x ( k + kt ( ∂ T /∂x) + ∂/∂y ( k +
kt ( ∂ T /∂y) + ∂/∂z ( k + kt ( ∂ T /∂z) (5)
The terms of turbulent diffusivities like µt
and kt are handled by two equation based turbulence
model- Realizable k-ε model. The realizable k-ε

16 | P a g e
model has distinct feature and that is the turbulent
dissipation rate equation is derived in such way that
conservation of mean square of vorticity is
guaranteed [ 6] . Readers are also directed to ref [7]
for further clarification.
Results of turbulent flows strongly depend
on near wall treatment. Near wall quantities are
modeling with the effective usage of blending
functions. This approach is often referred to as –
“Enhanced Wall Treatment” in various literature o
commercial CFD like reference- [7].
The numerical algorithm to solve the set of
partial differential equations is as described by
Patankar [8]. The convection terms are discretized
using Second Order Upwind scheme and SIMPLE
algorithm is used to handle pressure-velocity
coupling in Momentum equations.
Boundary conditions are deployed in such
way that at the inlet of channel known velocity is
specified and the channel is assumed to be open to
atmospheric pressure; stream-wise gradient of
temperature is assumed to be vanishing at outlet. A
constant heat flux boundary condition is specified to
represent the assembly of finned plate which is
subject subjected to appropriate conjugate heat
transfer conditions at the solid-air interfaces.
Properties like density, thermal conductivity in Eq
(5) are assumed to be varying subjected to solid or
fluid continuum zone.
Fig.1 A sample mesh for finned array.
Fig.1 shows a typical mesh for finned array and
some part of surrounding duct.
III. EXPERIMENTATION
Forced convection cooling is produced by
using a blower, the fin arrays are placed in a duct
90mm X 90mm X 1000mm long. The blower is
controlled by using a dimmerstat to adjust the flow
rate for each experiment. The air velocity is
recorded by using anemometer 100mm upstream of
the heatsink. Flat heater pad of nichrome wire were
attached to the bottom of heatsink with constant flux
heating on which arrays of Aluminium pinfin are
placed. Polycarbonate sheets are placed below the
heater pad to minimize the heat loss from the
bottom. Net Input flux can be calculated by
subtracting the heat loss occurring from the bottom
surface. The conduction heat loss at the bottom is
calculated by sensing the temperatures at the top and
bottom of polycarbonate sheet.
IV. RESULTS
Results are reported in terms variation of
Nusselt number (Nu) with respect to Reynolds
number and Grashof number for all three
configurations and heat transfer coefficient and
velocity . The length scale chosen for definition of
Reynolds and Nusself number is fin length (35 mm)
and velocity scale is inlet velocity.
Re = ρVL/μ; Nu= hL/k (6)
To define heat transfer coefficient, average surface
temperature of solid-fluid interface (Tave) and the
applied flux (q) is taken into account as described:
h(Tave – Tin) = q (7)
To define Grashof number, characteristic
temperature difference is based on heat flux as given
below :
Gr= gβΔTL3/ν2 ; ΔT = qL/k (8)
Since the problem assumes isoflux heating
to the fin base, regular definition of effectiveness of
fin is slightly modified. Effectiveness is defined as
the ratio of heat transfer coefficient with fins to the
heat transfer coefficient without fins. The above
definition of effectiveness can be named as
“Convective Effectiveness”.
3.1 Variation of Heat Transfer coefficient
The variation of heat transfer coefficient
with respect to air velocity is depicted in Fig. 2.
In all the configurations studied, it is found that
Heat Transfer Coefficient increases as Reynolds
number/Air velocity increase. This is due to the fact
that Reynolds number signifies the strength of
forced convection and, thus, increase of Heat
Transfer Coefficient with respect to rise in Reynolds
number is justified.

17 | P a g e
0
100
200
300
400
500
600
700
800
1 2.1 2.7 3.2
Heattransfercoefficient(W/m2K)
air velocities(m/s)
square exp
round exp
square cfd
round cfd
Fig. 2. Variation of Heat Transfer Coefficient
It can be seen from Fig 2 that for plane duct the
heat transfer coefficient is relatively smaller than
that would occur in other configurations. In plane
ducts, heat transfer occurs only via the thermal
boundary layer, while if flow is partially obstructed
(due to protrusions/fins), the mechanisms like
boundary layer separation, reattachement, shedding
of vortices become predominant and these
mechanisms contribute to the increase in the rate of
heat transfer.
3.2 Variation of Nusselt number
Since Nusselt number is directly
proportional to heat transfer coefficient, the
qualitative variation of Nusselt number against
Reynolds number remain same as that of the heat
transfer coefficient. As can be seen from the Figs . 3
and 4 Reynolds number increase, the strength of
forced convection increase and which in turn results
into the rise in Nusselt number.
Fig. 3 Variation of experimental Nusselt number with
Reynolds and Grashof number (Gr1= 3.3 X 107
Gr2= 4.1 X
107
, Gr3= 5 X 107
, Gr4 = 5.72 X 107
) for round
configuration.
It is also observed that increase in Grashof
number cause increase in Nusselt number, this is
attributed to the fact the buoyancy assists heat
transfer. However the dependence of Grashof
number is not as strong as that of the Reynolds
number. This is attributed to the fact that forced
convection washes out the heat directly while
naturally convection merely assists forced flow.
Fig. 4 Variation of CFD Based Nusselt number with
Reynolds and Grashof number (Gr1= 3.3 X 107
Gr2= 4.1 X 107
Gr3= 5 X 107
, Gr4 = 5.72 X
107
) for round configuration
Qualitatively, variation of numerically
obtained values of Nusselt number with respect to
Reynolds and Grashof number is same as observed
with experimental results. This is illustrated in Fig.
4.
TABLE. 1 Comparison of Nusselt number for
various configurations.
Gr1=
3.3 X
107
Gr2=
4.1 X
107
Gr3=
5 X
107
Gr4=
5.72 X
107
Square Configuration
Re=
2162
CFD 460 426 406 383
Expt 585.87 599.1 532.9 519.1
Re
=4540
CFD 537 506 483 475
Expt 648.1 621.85 596.1 570.96
Round Configuration
Re=
2162
CFD 322 352 406 415
Expt 402 476 483.1 523.1
Re
=4540
CFD 460 506 534 548
Expt 584.9 622 634 676.96
Out of many results obtained, Table 1 summarizes
various results at a glance. Following conclusions
can be reached :
1) Nusselt number predicted by CFD methods
and that observed by experimentation differ
easily by 20 to 30 percent. Without usage of
turbulence model, simulation resulted into
Nusselt number values 50 per cent lesser than
experimental values and at a times convergence
difficulties were encountered during simulations.

18 | P a g e
Choice of turbulence is always a matter of
debate, however, the presently chosen model has
a capability of blending the wall functions.
2) It is observed that Nusselt number values is
are on higher side than that of the circular fins.
3) The trends of variation of Nusselt number
with Grashof number for square configuration is
opposite than that of the trend observed in round
configuration. In round configuration, buoyancy
plays assisting role with enhancement of heat
transfer coefficient. However, the trends are
opposite for square fins.
V. CONCLUSION
The present paper is aimed at qualitative
and quantitative investigation of convective cooling
of fin arrays using numerical and experimental
appraoch. Comparison is made between square
shaped and round shaped fins. The results reveal
that heat transfer is higher in square configuration
that that obtained in round configuration. Surface
temperature based heat transfer coefficient and
Nusselt number monotonously increase with the
increase in Reynolds number, variation of these
quantities with Grashof number exhibit complicated
nature. The turbulence is well resolved by
Realizable k-ε model with blending function
approach for near wall treatment. However, still
difference of 20 to 30 percentage is seen to be
prevalent for experimental and numerical results.
REFERENCES
[1] G.N. Ellison, Thermal Computations for
Electronic Equipment, 2nd ed., Van Nostrand
Reinhold Corporation, New York, 1989
[2] A.D. Kraus, A. Bar-Cohen, Thermal Analysis
and Control of Electronic Equipment,
(Hemisphere Publishing Corporation,
Washington, 1983).
[3] M. Iyengar, A. Bar-Cohen, Least-energy
optimization of forced convection plate-fin
heat sinks, IEEE Trans Components and
Packaging Technologies 26 (2003) 62–70.
[4] K. Park, D.H. Choi, K.S. Lee, Optimum
design of plate heat exchanger with staggered
pin arrays, Numerical Heat Transfer. Part A,
Applications 45 (2004) 347–361.
[5] R.W. Keyes, “Heat Transfer in Forced
Convection Through Fins,” IEEE
Transactions on Electronic Devices, Vol.
ED-31, No, 9, pp. 1218-1221, 1984.
[6] T.-H. Shih, W. W. Liou, A. Shabbir, Z. Yang,
and J. Zhu. A New - Eddy-Viscosity
Model for High Reynolds Number Turbulent
Flows - Model Development and Validation.
Computers Fluids, 24(3):227-238, 1995.
[7] User Guide of FLUENT software, Chapter
12, Turbuelnce Modelling
[8] S.V. Patankar, Numerical Heat Transfer and
Fluid Flow. (McGraw-Hill, New York,
1980).

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